Comment:
Transformation from MAXIMUM 3-SATISFIABILITY.
In the weighted case, the problem is approximable within
for any
[30].
Admits a PTAS for `planar' instances [386].
Variation in which the number of occurrences of any element in X, Y or
Z is bounded by a constant B is APX-complete for
[280].
The generalized Maximum k-Dimensional Matching problem is
approximable within
for any
[265], and within 2(k+1)/3 in the weighted case.
The constrained variation in which the input is extended with a subset
S of T, and the problem is to find the 3-dimensional matching
that contains the largest number of elements from S,
is not approximable within
for some
[476].